Twisted rational zeros of linear recurrence sequences
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866914639553495040 |
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| author | Bilu, Yuri Luca, Florian Nieuwveld, Joris Ouaknine, Joël Worrell, James |
| author_facet | Bilu, Yuri Luca, Florian Nieuwveld, Joris Ouaknine, Joël Worrell, James |
| contents | We introduce the notion of a twisted rational zero of a non-degenerate linear recurrence sequence (LRS). We show that any non-degenerate LRS has only finitely many such twisted rational zeros. In the particular case of the Tribonacci sequence, we show that $1/3$ and $-5/3$ are the only twisted rational zeros which are not integral zeros. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_06537 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Twisted rational zeros of linear recurrence sequences Bilu, Yuri Luca, Florian Nieuwveld, Joris Ouaknine, Joël Worrell, James Number Theory 11D04 We introduce the notion of a twisted rational zero of a non-degenerate linear recurrence sequence (LRS). We show that any non-degenerate LRS has only finitely many such twisted rational zeros. In the particular case of the Tribonacci sequence, we show that $1/3$ and $-5/3$ are the only twisted rational zeros which are not integral zeros. |
| title | Twisted rational zeros of linear recurrence sequences |
| topic | Number Theory 11D04 |
| url | https://arxiv.org/abs/2401.06537 |